Giá trị của \(H = \frac{{38}}{{25}} + \frac{9}{{10}} - \frac{{11}}{{15}} + \frac{{13}}{{21}} - \frac{{15}}{{28}} + \frac{{17}}{{36}} - \ldots + \frac{{197}}{{4851}} - \frac{{199}}{{4950}}\) là
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Lời giải:
Báo sai\(\begin{array}{l} H = \frac{{38}}{{25}} + \frac{9}{{10}} - \frac{{11}}{{15}} + \frac{{13}}{{21}} - \frac{{15}}{{28}} + \frac{{17}}{{36}} - \ldots + \frac{{197}}{{4851}} - \frac{{199}}{{4950}}\\ \frac{H}{2} = \frac{{38}}{{50}} + \frac{9}{{20}} - \frac{{11}}{{30}} + \frac{{13}}{{42}} - \frac{{15}}{{56}} + \ldots + \frac{{197}}{{9702}} - \frac{{199}}{{9900}}\\ \frac{H}{2} = \frac{{38}}{{50}} + \frac{9}{{4.5}} - \frac{{11}}{{5.6}} + \frac{{13}}{{6.7}} - \frac{{15}}{{7.8}} + \ldots + \frac{{197}}{{98.99}} - \frac{{199}}{{99.100}}\\ \frac{H}{2} = \frac{{38}}{{50}} + \left( {\frac{1}{4} + \frac{1}{5}} \right) - \left( {\frac{1}{5} + \frac{1}{6}} \right) + \left( {\frac{1}{6} + \frac{1}{7}} \right) - \left( {\frac{1}{7} + \frac{1}{8}} \right) + \ldots + \left( {\frac{1}{{98}} + \frac{1}{{99}}} \right) - \left( {\frac{1}{{99}} + \frac{1}{{100}}} \right)\\ \frac{H}{2} = \frac{{38}}{{50}} + \frac{1}{4} - \frac{1}{{100}} = \frac{{76 + 25 - 1}}{{100}} = 1 \Rightarrow H = 2 \end{array}\)
